Figure 2 shows that both the multi-beta multi-strategy EW and ERC indexes present returns that are close to the average returns of the constituents but lower absolute and relative risk than the average constituent index. Both allocations thus deliver improvements in risk-adjusted returns compared to the average constituent index. One should note that the EW allocation delivers the highest Sharpe ratio (0.52 in the U.S., 0.56 in the developed universe) which, compared to the broad cap-weighted reference (0.24 in the U.S., and 0.36 in developed universe), represents a relative Sharpe ratio gain vof 115 percent in the U.S. data and more than 50 percent in the developed universe. One can also note that the allocation across several smart-factor indexes allows the tracking error to be reduced with respect to the cap-weighted reference index. Indeed, one witnesses impressive improvements for the multifactor allocations compared to the average of their component indexes in terms of relative risk, where both in the U.S. and in the developed universe, the reduction in the tracking error is around 0.70 percent for the EW allocation and 1 percent for the ERC allocation (which represent a risk reduction of about 11.5 percent for the EW allocation and more than 16 percent for the ERC allocation relative to the average tracking error of the component indexes in the U.S. case). This tracking error reduction yields an increase in the information ratios to levels of 0.76 and 0.77 from an average information ratio for the constituent indexes of 0.67 in the U.S., while in the developed region the average constituent information ratio is 0.78 and the multi-beta indexes deliver even higher information ratios, of 0.98 and 1.05, respectively, for the EW and ERC allocations. Such improvements in the information ratio, of 26 percent and 35 percent for the EW and ERC allocations, respectively, in the developed universe, are considerable and support the idea of diversification between smart factors. Moreover, compared to the average of their constituent indexes, the multi-beta multi-strategy indexes also exhibit significantly lower extreme relative risk (95 percent tracking error and maximum relative drawdown). In the developed universe, the maximum relative drawdowns of the multi-beta indexes are actually lower than those of any of the constituent indexes. It is noteworthy that—due to its focus on balancing relative risk contributions of constituents—the ERC allocation provides greater reductions in the relative risk measures such as the tracking error and the extreme tracking error risk.

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Briefly stated, the multi-beta allocations provide the average level of returns of their component indexes. However, factor diversification leads to a risk reduction that is particularly strong in relative terms, which eventually results in risk-adjusted performance that is well above average. Additionally, the benefits of allocation across different factors can be seen in the probability of outperformance, which is the historical frequency with which the index will outperform its cap-weighted reference index for a given investment horizon. The results in Figure 2 suggest that the probability of outperformance increases substantially for the multi-beta indexes compared with the average across component indexes, especially at short horizons. The higher probabilities of outperformance reflect the smoother and more robust outperformance resulting from the combination of different rewarded factors within a multi-beta index. The outperformance of multifactor allocations is further analysed in Figures 3, 4 and 5.